A repairable product under a non-renewing combined warranty policy that is subject to a displaced log-linear demand function of the product's price and pro rata period length is considered. Expressions for the manufacturer's long-run average profit per unit time under replacement, minimal and general repair options are obtained. In addition, expressions for the stationary points and second-order conditions of the profit function are presented. Numerical illustrations that demonstrate optimal product pricing, pro rata length determination, and repair option selection to maximize the manufacturers, profit are given.

No abstract

Two-dimensional renewal functions, which are naturally extensions of one-dimensional renewal functions, have wide applicability in areas where two random variables are needed to characterize the underlying process. These functions satisfy the renewal equation, which is not amenable for analytical solutions. This paper proposes a simple approximation for the computation of the two-dimensional renewal function based only on the first two moments and the correlation coefficient of the variables. The approximation yields exact values of renewal function for bivariate exponential distribution function. Illustrations are presented to compare our approximation with that of Iskandar (1991) who provided a computational procedure which requires the use of the bivariate distribution function of the two variables. A two-dimensional warranty model is used to illustrate the approximation.

No abstract

Purpose -The purpose of this paper is to generalize Yeh and Zhang's 2004 random threshold failure model for deteriorating systems. Design/methodology/approach -An N-policy was adopted by which the system was replaced after the Nth failure. Findings -The model was found to have practical applications in warranty cost analysis. Originality/value -By identifying the instance of a shock as the failure of the system and the threshold times as the warranty period offered and changing the definition of lethal shock (system failure in this case) as the occurrence of a shock within a threshold period in our generalized model, one can study the renewing warranty cost analysis.

A system is subject to shocks; each shock at time t increases the cumulative damage λ (t) by a constant amount, while the system is subject to repair in between the shocks which brings down λ (t) at a constant rate. The shock arrival process is an inhomogeneous Poisson process with intensity function λ (t) and each shock weakens the system making it more expensive to run. The long-run expected cost per unit time of running the system is obtained as well as the variance of the cost which are used to get optimal times of replacement of the system.

A system is subject to shocks; each shock at time t increases the cumulative damage λ (t) by a constant amount, while the system is subject to repair in between the shocks which brings down λ (t) at a constant rate. The shock arrival process is an inhomogeneous Poisson process with intensity function λ (t) and each shock weakens the system making it more expensive to run. The long-run expected cost per unit time of running the system is obtained as well as the variance of the cost which are used to get optimal times of replacement of the system.

A system is repaired on failure. With probability p, it is returned to the 'good as new' state (perfect repair) and with probability 1 -p, it is returned to the functioning state, but is only as good as a system of age equal to its age at failure (imperfect repair). In this article, we develop replacement policies for a deteriorating system with imperfect maintenance. The successive survival times and consecutive repair times form a geometric process which is stochastically non-increasing or non-decreasing respectively. Explicit expressions are obtained for the long-run expected cost under two kinds of replacement policies based on the working age of the system and the number of imperfect repairs before a replacement.